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## Summary

700 (seven hundred) is the natural number following 699 and preceding 701.

 ← 699 700 701 →
Cardinalseven hundred
Ordinal700th
(seven hundredth)
Factorization22 × 52 × 7
Greek numeralΨ´
Roman numeralDCC
Binary10101111002
Ternary2212213
Octal12748
Duodecimal4A412

It is the sum of four consecutive primes (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317) and a Harshad number.

## Integers from 701 to 799

Nearly all of the palindromic integers between 700 and 800 are used as model numbers for Boeing Commercial Airplanes, and the only one not officially used by Boeing, 797, is commonly speculated to be the number of the next new Boeing commercial airplane.

### 710s

• 710 = 2 × 5 × 71, sphenic number, nontotient, number of forests with 11 vertices 
• 711 = 32 × 79, Harshad number, number of planar Berge perfect graphs on 7 nodes. Also the phone number of Telecommunications Relay Service, commonly used by the deaf and hard-of-hearing.
• 712 = 23 × 89, sum of the first twenty-one primes, totient sum for first 48 integers. It is the largest known number such that it and its 8th power (66,045,000,696,445,844,586,496) have no common digits.
• 713 = 23 × 31, blum integer, main area code for Houston, TX. In Judaism there is 713 letters on a Mezuzah scroll.
• 714 = 2 × 3 × 7 × 17, sum of twelve consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), nontotient, balanced number, member of Ruth–Aaron pair (either definition); area code for Orange County, California.
• 714 is the number of career home runs hit by Babe Ruth, a record that stood from his last home run on May 25, 1935, until being broken by Hank Aaron on April 8, 1974.
• Flight 714 to Sidney is a Tintin graphic novel.
• 714 is the badge number of Sergeant Joe Friday.
• 715 = 5 × 11 × 13, sphenic number, pentagonal number, pentatope number ( binomial coefficient ${\tbinom {13}{4}}$  ), Harshad number, member of Ruth-Aaron pair (either definition)
• The product of 714 and 715 is the product of the first 7 prime numbers (2, 3, 5, 7, 11, 13, and 17)
• 716 = 22 × 179, area code for Buffalo, NY
• 717 = 3 × 239, palindromic number, model number for the Boeing 717
• 718 = 2 × 359, area code for Brooklyn, NY and Bronx, NY
• 719 = prime number, factorial prime (6! − 1), Sophie Germain prime, safe prime, sum of seven consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part

### 740s

• 740 = 22 × 5 × 37, nontotient, number of connected squarefree graphs on 9 nodes 
• 741 = 3 × 13 × 19, sphenic number, triangular number
• 742 = 2 × 7 × 53, sphenic number, decagonal number, icosahedral number. It is the smallest number that is one more than triple its reverse. Lazy caterer number (sequence A000124 in the OEIS). Number of partitions of 30 into divisors of 30.
• 743 = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part
• 744 = 23 × 3 × 31, sum of four consecutive primes (179 + 181 + 191 + 193). It is the coefficient of the first degree term of the expansion of Klein's j-invariant. Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebra E8.
• 745 = 5 × 149 = 24 + 36, number of non-connected simple labeled graphs covering 6 vertices
• 746 = 2 × 373 = 15 + 24 + 36 = 17 + 24 + 36, nontotient, number of non-normal semi-magic squares with sum of entries equal to 6
• 747 = 32 × 83 = $\lfloor {\frac {4^{23}}{3^{23}}}\rfloor$ , palindromic number, model number of the Boeing 747 jet airliner
• 748 = 22 × 11 × 17, nontotient, happy number, primitive abundant number
• 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257), blum integer

### 750s

• 750 = 2 × 3 × 53, enneagonal number.
• 751 = prime number, Chen prime
• 752 = 24 × 47, nontotient, number of partitions of 11 into parts of 2 kinds
• 753 = 3 × 251, blum integer
• 754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers, number of different ways to divide a 10 × 10 square into sub-squares 
• 755 = 5 × 151, number of vertices in a regular drawing of the complete bipartite graph Kn,n. In 1976, Major League Baseball player Hank Aaron ended his career with a Major League record 755 home runs (record now held by Barry Bonds).
• 756 = 22 × 33 × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number, Harshad number
• 757 = prime number, palindromic prime, sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127), happy number, model number for the Boeing 757
• 758 = 2 × 379, nontotient, prime number of measurement 
• 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163), a q-Fibonacci numbers for q=3 

### 770s

• 770 = 2 × 5 × 7 × 11, nontotient, Harshad number
• $\sum _{n=0}^{10}770^{n}$  is prime
• Famous room party in New Orleans hotel room 770, giving the name to a well known science fiction fanzine called File 770
• Holds special importance in the Chabad-Lubavitch Hasidic movement.
• 771 = 3 × 257, sum of three consecutive primes in arithmetic progression (251 + 257 + 263). Since 771 is the product of the distinct Fermat primes 3 and 257, a regular polygon with 771 sides can be constructed using compass and straightedge, and $\cos \left({\frac {2\pi }{771}}\right)$  can be written in terms of square roots.
• 772 = 22 × 193, 772!!!!!!+1 is prime
• 773 = prime number, Eisenstein prime with no imaginary part, tetranacci number, prime index prime
• 774 = 2 × 32 × 43, nontotient, totient sum for first 50 integers, Harshad number
• 775 = 52 × 31, member of the Mian–Chowla sequence, happy number
• 776 = 23 × 97, number of compositions of 6 whose parts equal to q can be of q2 kinds

### 780s

• 780 = 22 × 3 × 5 × 13, sum of four consecutive primes in a quadruplet (191, 193, 197, and 199); sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), triangular number, hexagonal number, Harshad number
• 780 and 990 are the fourth smallest pair of triangular numbers whose sum and difference (1770 and 210) are also triangular.
• 781 = 11 × 71, sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0, lazy caterer number (sequence A000124 in the OEIS)
• 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number, Harshad number, also, 782 gear used by U.S. Marines
• 783 = 33 × 29, heptagonal number
• 784 = 24 × 72 = 282 = $1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}+7^{3}$ , the sum of the cubes of the first seven integers, happy number
• 785 = 5 × 157, Mertens function(785) = 0, number of series-reduced planted trees with 6 leaves of 2 colors 

### 790s

• 790 = 2 × 5 × 79, sphenic number, nontotient
• 791 = 7 × 113, centered tetrahedral number, sum of the first twenty-two primes, sum of seven consecutive primes (101 + 103 + 107 + 109 + 113 + 127 + 131)
• 792 = 23 × 32 × 11, number of partitions of 21, binomial coefficient ${\tbinom {12}{5}}$ , Harshad number, sum of the nontriangular numbers between successive triangular numbers
• 793 = 13 × 61, Mertens function(793) = 0, star number, happy number
• 794 = 2 × 397 = 16 + 26 + 36, nontotient
• 795 = 3 × 5 × 53, Mertens function(795) = 0, number of permutations of length 7 with 2 consecutive ascending pairs 
• 796 = 22 × 199, sum of six consecutive primes (113 + 127 + 131 + 137 + 139 + 149), Mertens function(796) = 0
• 797 = prime number, Chen prime, Eisenstein prime with no imaginary part, palindromic prime, two-sided prime, prime index prime, speculated model number for the Boeing New Midsize Airplane
• 798 = 2 × 3 × 7 × 19, Mertens function(798) = 0, nontotient, product of primes indexed by the prime exponents of 10! 
• 799 = 17 × 47, smallest number with digit sum 25